High School Physics: Doppler Effect

[Litterus]

Homework Statement

An automobile is approaching you at a speed of 60.0 km/h and sounding its horn. The fundamental frequency of the horn sounds to you like 388 Hz. If the real fundamental frequency of the horn is 369 Hz, what is the speed of sound?

Homework Equations

Doppler Frequency = (speed of sound / (speed of sound - speed of source)) source frequency

f_d = (v_w/ v_w - v_s) f_s

The Attempt at a Solution

What I'm having trouble with is rearranging the formula to solve for the speed of sound. Because there is two 'speed of sound' variables, you either end up dividing one by the other, and eliminating all variables; or subtracting one from the other, and (once again) eliminating all variables. As far as I can see, it's not possible?

Could someone help me out with rearranging this formula properly?

In case anyone's wondering, it's Grade 11 Physics.

 

[Tusike]

You have the formula written down wrong.

You wrote:

fd = (vw/ vw - vs) fs

It's supposed to be:

fd = (vw / (vw - vs)) fs

Good luck!

 

[Filip Larsen]

Try multiply both sides of the equation (when its written up correctly as Tusike noted) with v_w-v_s. The resulting equation should now be easier to solve for v_w.

 

[Litterus]

Thanks alot! I got the correct answer, thanks to both of those pieces of advice.

 

[rwisz]

Dear student,

Thank you for your question. The Doppler effect is a phenomenon that is observed when there is relative motion between a source of sound and the observer. In this case, the source of sound is the automobile and the observer is you.

To solve for the speed of sound, we can use the formula you provided: fd = (vw/ vw - vs) fs

First, let's rearrange the formula to solve for the speed of sound:

vw = (fd * (vw - vs)) / fs

Now, we can substitute the given values into the formula:

vw = (388 Hz * (60.0 km/h - 0 km/h)) / 369 Hz

vw = 62.6 km/h

This is the velocity of the wave relative to the observer. Since the observer is stationary, this is also the speed of sound.

Therefore, the speed of sound is 62.6 km/h.

I hope this helps. Keep up the good work in your physics studies!

Best,

Scientist